Question

Integrate: ( log sinx ) / tanx

Answer 1

$\bold{\int {\frac{log (sinx)}{tanx}} \, dx }$

$\bold{\int {\frac{(cos x)log (sinx)}{sinx}} \, dx }$

$\bold{log(sin x) =t}$

$\bold{\frac{cosx}{sinx} = dt}$

$\bold{\int\ {t} \, dt}$

$\bold {=\frac{t^2}{2}+ C}$

Answer 2

Hi,

Here is your answer,

Questtion = (log sinx)/tax

INTEGRATE

∫log(sinx)/tanx. dx

∫ (cosx).log(sinx)/sinx. dx

Let us consider log(sinx) = z

cosx/sinx = z

→ ∫zdz = z²/2 + c

Hope it helps you !